Each shot of the laser gun most favored by Rosa the Closer, the intrepid vigilan

Question

Each shot of the laser gun most favored by Rosa the Closer, the intrepid vigilante of the lawless 22nd century, is powered by the discharge of a 1.31-F capacitor charged to 67.1 kV. Rosa rightly reckons that she can enhance the effect of each laser pulse by increasing the electric potential energy of the charged capacitor. This she would do by replacing the capacitor's filling, whose dielectric constant is 477, with one possessing a dielectric constant of 945. Find the electric potential energy of the original capacitor when it is charged. Calculate the electric potential energy of the upgraded capacitor when it is charged.

Explanation / Answer

Initially:

C = 1.31 F and V = 67100 V

PE = CV^2 / 2 = (1.31 x (67.1 x 10^3)^2)/2 = 2.95 x 10^9 J

and PD remains constant.

C = ke0A/d = kC0

initial C = 477C0

finally C' = 945 C0

so C' = (945/477)C = 2.595 F

finally PE = 2.595 x (67100)^2 /2 = 5.84 x 10^9 J

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